{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T06:01:16Z","timestamp":1774159276892,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T00:00:00Z","timestamp":1773964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NRF Incentive Funding for Rated Researchers","award":["97822"],"award-info":[{"award-number":["97822"]}]},{"DOI":"10.13039\/501100008976","name":"University of Venda","doi-asserted-by":"crossref","award":["R018"],"award-info":[{"award-number":["R018"]}],"id":[{"id":"10.13039\/501100008976","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Research Foundation of South Africa","award":["132108"],"award-info":[{"award-number":["132108"]}]},{"name":"University of the Witwatersrand"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The full symmetry group is found for a system of nonlinear schr\u00f6dinger equations describing the propagation of optical pulses in an isotropic media. It is shown, in particular, that the six-dimensional symmetry group found is composed of a scaling transformation and a rotation of the four-dimensional space, thereby proving that the symmetry group preserves the shape of solutions. A symmetry classification of one-dimensional subalgebras of the Lie algebra is performed and yields, in particular, the symmetry reduction to the most general system of equations satisfied by the solitary waves of the equation. Explicit soliton solutions of the equation are found by largely autonomous technics. The found solitons are used to recursively generate two new ones by means of two iterations using the symmetry group. Other properties of the system are also highlighted, as well as the possible connections between the theories of symmetry groups and Darboux transformations inspired by this study.<\/jats:p>","DOI":"10.3390\/axioms15030231","type":"journal-article","created":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T09:44:41Z","timestamp":1773999881000},"page":"231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetry Transformations of a Nonlinear Model of Optical Wave Transmission"],"prefix":"10.3390","volume":"15","author":[{"given":"Jean-Claude","family":"Ndogmo","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computational Sciences, University of Venda, P.O. Box 5050, Thohoyandou 0950, South Africa"}]},{"given":"Emmanuel Mayombo","family":"Mbala","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, University of Venda, P.O. Box 5050, Thohoyandou 0950, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3046-0679","authenticated-orcid":false,"given":"Mensah Kekeli","family":"Folly-Gbetoula","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Braamfontein, Johannesburg 2017, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1038\/nature01935","article-title":"A revolution in optical manipulation","volume":"424","author":"Grier","year":"2003","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"106620","DOI":"10.1016\/j.optlastec.2020.106620","article-title":"Recent optical sensing technologies for the detection of various biomolecules: Review","volume":"134","author":"Kumar","year":"2021","journal-title":"Opt. 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